re: rotafix....come on, that cog is going to come off eventually. Why risk it? And the man said he wants a fixed, not a single speed. Leaving the freewheel on is a lame suggestion.
Basically, if you want to do a fixed conversion right, it's going to take at least a new set of wheels. Relacing an old wheel and spokes to a new hub is sketchy, esp with a 27" wheel from the '70s...